Question

The r.m.s. speed of the molecules of a gas at $100^{\circ }C$ is $\nu$. The temperature at which the r.m.s. speed will be $\sqrt{3}v$ is

• A. 546${}^{\circ }$C
• B. 646${}^{\circ }$C
• C. 746${}^{\circ }$C
• D. 846${}^{\circ }$C

Answer 1

Answer: (D)

$v_{ms}=\sqrt{\frac{3RT}{M}}$
Given, $T=100^{\circ }C=373K$
$\therefore v=\sqrt{\frac{3R\times 373}{M}}$
For $\sqrt{3}v=\sqrt{\frac{3RT}{M}}$
$\therefore \frac{\sqrt{3}V}{V}=\frac{\sqrt{3RT/M}}{\sqrt{3R\times 373/M}}$
$\Rightarrow \sqrt{3}=\sqrt{\frac{T}{373}}$
$\Rightarrow 3=\frac{T}{373}$
$\Rightarrow T=1119K$
or $T=846^{\circ }C$